We prove quantitative isoperimetric inequalities for images of the unit ball under homeomorphisms of exponentially integrable distortion. We show that the metric distortions of such domains can be controlled by their Fraenkel asymmetries. An application of the quantitative isoperimetric inequality proved by Hall and Fusco, Maggi, and Pratelli then shows that for these domains a version of Bonnesen’s inequality holds in all dimensions.
@article{ASNSP_2012_5_11_1_177_0, author = {Rajala, Kai}, title = {Quantitative isoperimetric inequalities and homeomorphisms with finite distortion}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {177--196}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 11}, number = {1}, year = {2012}, mrnumber = {2953048}, zbl = {1264.30016}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2012_5_11_1_177_0/} }
TY - JOUR AU - Rajala, Kai TI - Quantitative isoperimetric inequalities and homeomorphisms with finite distortion JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2012 SP - 177 EP - 196 VL - 11 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2012_5_11_1_177_0/ LA - en ID - ASNSP_2012_5_11_1_177_0 ER -
%0 Journal Article %A Rajala, Kai %T Quantitative isoperimetric inequalities and homeomorphisms with finite distortion %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2012 %P 177-196 %V 11 %N 1 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2012_5_11_1_177_0/ %G en %F ASNSP_2012_5_11_1_177_0
Rajala, Kai. Quantitative isoperimetric inequalities and homeomorphisms with finite distortion. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 1, pp. 177-196. http://archive.numdam.org/item/ASNSP_2012_5_11_1_177_0/
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